From Q-walls to Q-balls

We study $Q$-ball type solitons in arbitrary spatial dimensions in thesetting recently described by Kusenko, where the scalar field potential has aflat direction which rises much slower than $\phi^2$. We find that the generalformula for energy as a function of the charge is, $E_d\sim Q_d^{(d/d+1)}$ inspatial dimension $d$. We show that the Hamiltonian governing the stabilityanalysis of certain $Q$-wall configurations, which are one dimensional $Q$-ballsolutions extended to planar, wall-like configurations in three dimensions, canbe related to supersymmetric quantum mechanics. $Q$-wall and $Q$-string (thecorresponding extensions of 2 dimensional $Q$-balls in 3 spatial dimensions)configurations are seen to be unstable, and will tend to bead and form planaror linear arrays of 3 dimensional $Q$-balls. The lifetime of these wall-likeand string-like configurations is, however, arbitrarily large and hence theycould be of relevance to cosmological density fluctuations and structureformation in the early Universe.Comment: 20 pages, 2 figure